Recall that we say that lim f (x) = L if the (output) values, f(x), of ƒ get arbitrarily close to L as its input values approach a. “Arbitrarily close" means "as close as anyone might ever mandate", very loosely speaking. Please label the following statements as being true or false. Make sure you support your answer with a sketch. (a) If a is not in the domain of f , then lim f(x) is undefined. (b) If lim f() = 0 and lim f(x) = 3, lim f (x) might still be defined. x-a+ (c) If lim f(x) = f(a), then the graph of y = f (x) is continuous at x = a. %3D

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.